$J$-Domination in Graphs


  • Javier Hassan MSU Tawi-Tawi College of Technology and Oceanography
  • Jeffrey Imer Salim




J-set, J-dominating set, J-domination number


Let $G$ be a graph. A subset $D=\{d_1, d_2, \cdots, d_m\}$ of vertices of $G$ is called a $J$-set if $N_G[d_i]\setminus N_G[d_j]\neq \varnothing$ for every $i\neq j$, where $i,j\in\{1, 2, \ldots, m\}$. A $J$-set is called a $J$-dominating set of $G$ if $D=\{d_1, d_2, \ldots, d_m\}$ is a dominating set of $G$. The $J$-domination number of $G$, denoted by $\gamma_{J}(G)$, is the maximum cardinality of a $J$-dominating set of $G$. In this paper, we introduce this new concept and we establish formulas and properties on some classes of graphs and in join of two graphs. Upper and lower bounds of $J$-domination parameter with respect to the order of a graph and other parameters in graph theory are obtained. In addition, we present realization result involving this parameter and the standard domination. Moreover, we characterize $J$-dominating sets in some classes of graphs and join of two graphs and finally determine the exact value of the parameter of each of these graphs.






Nonlinear Analysis

How to Cite

$J$-Domination in Graphs. (2023). European Journal of Pure and Applied Mathematics, 16(4), 2082-2095. https://doi.org/10.29020/nybg.ejpam.v16i4.4883

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